When you receive a DMCA notice you can respond with a counter-claim notice that says the claim is incorrect and that you're willing to go to court about it. This could be because you have distribution rights, because of fair use, or for any other reason that would make the claim invalid. The copyright holder then has 14 days to file a case to sue the alleged infringing party. If they don't, the notice can be ignored and any third party host must restore access to the files.
Whether these files should be accessible under fair use, I don't know, but at that point it's up to the court.
Point being, if you file a counter-claim you're basically saying go ahead and sue me then. If a company with deep pockets has a reason to think they can enforce the claim, they probably will take you to court. Even if you win, you're going to have to pay for a lawyer and deal with a court case.